# Eelbode+Hitzer: Operator Exponentials for the Cli fford Fourier Transform on Multivector Fields

Authors: David Eelbode, Eckhard Hitzer

Abstract: This paper briefly reviews the notion of Clifford’s geometric algebras and vector to multivector functions; as well as the field of Clifford analysis (function theory of the Dirac operator). In Clifford Fourier transformations (CFT) on multivector signals the complex unit $i \in \mathbb{C}$ is replaced by a multivector square root of $-1$, which may be a pseudoscalar in the simplest case. For these transforms we derive, via a multivector function representation in terms of monogenic polynomials, the operator representation of the CFTs by exponentiating the Hamilton operator of a harmonic oscillator.

Comments: Submitted to Publications of Research Institute for Mathematical Sciences (PRIMS), March 2014, 18 pages.